Resuming the evening 10-6 clear, Welshman Jones looked to be in danger of collapsing under the weight of expectation as 2007 Welsh Open finalist Higginson won four straight frames to level at 10-10 boosted by knocks of 54, 41, 53 and 41.
The pressure seemed to transfer onto the shoulders of Higginson from that point onwards as the Widnes player compiled a disappointing 37 points in the final three frames with Jones emulating the form that accounted for Shaun Murphy in the first round as runs of 50, 135 and 42 secured a quarter-final match with Ali Carter.
Jones is the third Welshman into the last eight with Ryan Day facing Matthew Stevens in the top half of the draw.
Second session report
Jamie Jones moved 10-6 ahead in the battle of the qualifiers with Andrew Higginson in their second-round encounter at the Crucible Theatre, winning six of the eight frames in the evening session including a dramatic doubled black to finish it.
Welshman Jones, ranked 36, won the opening three frames to put Higginson in trouble at 7-4 down and, although the Englishman went on to take two frames in the session, Jones will be in control when they play to a finish on Monday evening.
A mistake from Higginson in the opening frame let Jones in and the Welshman knocked in a superb opening break of 95 to win his third frame on the trot.
Jones was in first again in frame 10 but missed a black off its spot to give Higginson a chance. However he missed a relatively simple black on 49 to allow Jones back in - and he polished off the remaining colours to secure another frame.
Higginson's opening break in the next frame ended at 33 with a missed blue and Jones pounced to take full advantage, nailing a superb plant to the middle on the way to a frame-winning break of 65.
A much-needed 89 break got Higginson up and running in the final frame before the mid-session interval. When they returned to the table he opened with a 26 before a missed red along the top rail; Jones made him pay with a break of 101 to once again go three frames ahead.
Jones looked to be cruising in the next frame before his break ended on 51 with a missed black off its spot. Higginson looked to have pinched the frame, needing the colours up to the pink, but somehow failed to pot a yellow off its spot - and Jones capitalised to go 9-5 clear.
It was Jones who got off to the better start in frame 15 but a loose safety allowed Higginson to reduce the arrears with a break of 82.
Higginson looked to be on his way again with a 57 break but once again he missed a simple black to let Jones in, the Welshman finishing with an incredible clearance culminating in a doubled black at 57-57 to lead 10-6 overnight.
First session report
Qualifiers Jamie Jones and Andrew Higginson are level at 4-4 after the first session of their World Championship second-round encounter at the Crucible Theatre.
The duo, who upset Shaun Murphy and Stephen Lee respectively to make it to the second round, traded the table frequently early on but it was the Welshman who finished the job on both of the first two occasions to lead 2-0.
Higginson would find his stride from there, holding off Jones's quest for snookers to claim his first of the contest before racking up another three for a lead of four frames to two, breaking over 50 in the fifth and sixth.
But Jones ensured the encounter would be back at square one come the evening session when he claimed the final two frames of the session, putting an exclamation mark on things in the form of a 72 break to secure frame eight.
A break of 43 would prove the nexus of Jones claiming the opening frame, though a tough table forced him to edge his way over the finish line despite stubborn resistance from Higginson, who would go on to fall two behind when Jones took control in the second and clear to the final pink.
The Englishman's own 43 would send him on his way to pulling one back, before a run to 31 was the highest of a scrappy fourth.
Two half-tons, clocking in at 59 and 54, made it four frames on the spin for the 34-year old, though Jones would fight to the bitter end in hope of 3-3 in search of two snookers with just pink and black left.
But the Welsh youngster would retaliate with a fantastic long pink clinching another back-and-forth affair for 4-3 before finishing the session with breaks of 28 and 72 to level up once more.